Mechatronics & Robotics

Electronic Cam Synchronization Analyzer — Phase Error, Stability Ratio & Max Sync Speed Calculator

Calculate estimated phase error using master speed, gear ratio, servo bandwidth, system delay, profile type, and sync mode.

Unit-aware inputs Deterministic calculation Engineering interpretation
Calculation workspace

Enter the known values and review the calculated result

Deterministic calculation
01
Parameters

Input parameters

Use consistent values and select the intended engineering units.

Synchronization mode

General parameters

Control system

Cam profile

Limits

02
Output

Results

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Engineering reference

Method, application and limitations

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01
Method

Formula and calculation method

Estimated phase error formula:

ωslave = ωmaster · i

Δφdyn =
(ωslave / (2π · fbw)) · 360 · kprofile · kmode

Δφdelay =
ωslave · τ · (180 / π)

Δφ = Δφdyn + Δφdelay

Synchronization stability ratio formula:

Δφ / Δφmax

Max sync speed formula:

ωmax =
(Δφmax · π / 180) /
(τ + 1 / (2π · fbw))

Profile factor:

  • Smooth: kprofile = 0.6
  • Standard: kprofile = 1.0
  • Aggressive: kprofile = 1.6

Mode factor:

  • Electronic gearing: kmode = 1.0
  • Electronic cam: kmode = 1.2

where:

  • Δφ — Estimated phase error (deg)
  • Δφdyn — Dynamic phase shift (deg)
  • Δφdelay — Delay phase shift (deg)
  • Δφmax — Max allowed phase error (deg)
  • ωmaster — Master speed (rad/s)
  • ωslave — Slave speed (rad/s)
  • ωmax — Max sync speed (rad/s)
  • i — Gear ratio (-)
  • fbw — Servo bandwidth (Hz)
  • τ — System delay (s)
  • kprofile — Profile factor (-)
  • kmode — Synchronization mode factor (-)
02
Application

When to use this calculator

When to use this calculator:

  • Estimate phase error for a slave axis synchronized to a master axis through electronic gearing.
  • Evaluate electronic cam synchronization when profile aggressiveness changes from smooth to standard or aggressive.
  • Check whether the estimated phase error stays below the allowed phase error limit.
  • Estimate the maximum synchronization speed allowed by servo bandwidth and system delay.
  • Identify whether synchronization is mainly affected by delay, insufficient bandwidth, dynamic phase shift, or aggressive profile selection.
03
Decision support

How to interpret the result

Estimated phase error is defined as the calculated angular mismatch between the synchronized slave motion and the master reference caused by dynamic response and system delay.

The synchronization stability ratio is defined as estimated phase error divided by the max allowed phase error. A lower ratio means more remaining synchronization margin. A higher ratio means the calculated phase error is closer to or above the allowed limit.

Max sync speed is defined as the highest synchronization speed allowed by the selected phase error limit, servo bandwidth, and system delay.

  • Safe — synchronization stability ratio is below 0.65.
  • Warning — synchronization stability ratio is at least 0.65 and below 0.85.
  • Limit — synchronization stability ratio is at least 0.85 and below 1.00.
  • Unsafe — synchronization stability ratio is at least 1.00.
  • Invalid — input data violates the JS validation rules for profile, mode, speed, ratio, cycle time, bandwidth, delay, max allowed phase error, or computed phase terms.

Increasing master speed, gear ratio, system delay, profile aggressiveness, or switching from electronic gearing to electronic cam increases estimated phase error. Increasing servo bandwidth decreases the dynamic part of estimated phase error.

04
Worked case

Calculation example

When to use this calculator:

  • Estimate phase error for a slave axis synchronized to a master axis through electronic gearing.
  • Evaluate electronic cam synchronization when profile aggressiveness changes from smooth to standard or aggressive.
  • Check whether the estimated phase error stays below the allowed phase error limit.
  • Estimate the maximum synchronization speed allowed by servo bandwidth and system delay.
  • Identify whether synchronization is mainly affected by delay, insufficient bandwidth, dynamic phase shift, or aggressive profile selection.
05
Model boundaries

Assumptions and limitations

  • The slave speed is calculated as master speed multiplied by gear ratio.
  • The dynamic phase shift depends on slave speed, servo bandwidth, profile factor, and synchronization mode factor.
  • The delay phase shift depends on slave speed and system delay converted to seconds.
  • The profile factor is fixed at 0.6 for smooth, 1.0 for standard, and 1.6 for aggressive.
  • The synchronization mode factor is fixed at 1.0 for electronic gearing and 1.2 for electronic cam.
  • The synchronization status is determined only by the synchronization stability ratio thresholds defined in the JS.
06
Questions

Frequently asked questions

How to calculate estimated phase error?
Estimated phase error is calculated as the sum of dynamic phase shift and delay phase shift. It depends on master speed, gear ratio, servo bandwidth, system delay, profile type, and synchronization mode. Increasing master speed, gear ratio, system delay, profile aggressiveness, or electronic cam mode increases estimated phase error. Increasing servo bandwidth decreases estimated phase error.
What affects estimated phase error the most?
Estimated phase error depends directly on slave speed, delay contribution, bandwidth contribution, profile factor, and mode factor. A higher slave speed increases both dynamic phase shift and delay phase shift. A higher servo bandwidth reduces dynamic phase shift. A higher system delay increases delay phase shift.
When is the estimated phase error formula not valid?
The formula is not valid when the selected profile is not smooth, standard, or aggressive, or when the selected mode is not electronic gearing or electronic cam. It is also not valid when master speed, gear ratio, cycle time, servo bandwidth, or max allowed phase error are less than or equal to zero, or when system delay is negative.
Can this calculator be used for electronic cam synchronization?
It can be used for electronic cam synchronization when the mode is set to electronic cam. In that mode, the phase error calculation applies a mode factor of 1.2, which increases the dynamic phase shift compared with electronic gearing.
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Engineering notice. Verify input data, assumptions, applicable standards and required safety factors before using results for design release or safety-critical decisions.