2021-12-30T14:38:33.000-0500

Simcenter SCADAS
Simcenter Testlab

YouTube Direct link: https://youtu.be/1-ExbIEqedw

Simcenter Testlab can be used to measure angular position (degrees) and rotational speed (revolutions per minute or rpm) from multiple and different types of encoder devices. Math can be performed between measurements made from different devices to determine the relative rotational speed and angular positions at locations along a drive system.

An example drive system with an electric motor is shown in this article. In this system, as the speed of the motor changes, an unwanted vibration occurs. An illustration of the system is shown in

To diagnose the issue, the windup (i.e., the difference in angular displacement in degrees) between the electric motor to the final drive encoder is calculated. The steps for performing these calculations using Simcenter Testlab are also explained in depth.

Index

*1. Overview*

2. Resolver

3. Rotational Speed versus Rotational Angle

4. Encoder: Moments versus RPM

5. Angular Difference Results

**1. Overview**

*Equation 1 *is used to calculate the the relative angular displacement between the electric motor shaft rotation and the final drive rotation:

Index

2. Resolver

3. Rotational Speed versus Rotational Angle

4. Encoder: Moments versus RPM

5. Angular Difference Results

Because there is a geared transmission unit between the electric motor and final drive, the gear ratio must be used to adjust the electric motor angular position relative to the final drive in order to calculate the difference.

The formulas used in the Simcenter Testlab Time Signal Calculator to calculate the angular difference are shown in*Figure 2*.

The formulas used in the Simcenter Testlab Time Signal Calculator to calculate the angular difference are shown in

The equations CH18 and CH 20 are not need but are performed to verify the correctness of the results. This is explained in the upcoming section "Rotational Speed versus Rotational Angle".

See the knowledge article "Time Signal Calculator Tips!" for information on using formulas for calculations.

The formulas are further explained in the next sections.

**2. Resolver**

This section details the formulas (*Figure 3*) used to calculate the angle position and rotational speed from the resolver on the electric motor.

See the knowledge article "Time Signal Calculator Tips!" for information on using formulas for calculations.

The formulas are further explained in the next sections.

This section details the formulas (

Electric motors are often equipped with resolvers (

There are several different types of resolvers, but most have three key signals:

- EXCITATION: Excitation voltage with carrier frequency.
- SINE: Sine wave proportional to one rotation of the shaft. The excitation frequency is modulated by this sine wave.
- COSINE: Cosine wave proportional to one rotation of the shaft. The excitation frequency is modulated by this cosine wave.

Examples of these three signals measured from a resolver are shown in *Figure 5*.

The signals are voltages composed of sine waves. The sine and cosine signal are amplitude modulated while the excitation signal is not.

The Simcenter Testlab Time Signal Calculator has specific functions for calculating rpm or angle from these resolver signals as shown in*Figure 6*.

The Simcenter Testlab Time Signal Calculator has specific functions for calculating rpm or angle from these resolver signals as shown in

The inputs to the method are as follows:

- function1: Cosine signal.
- function2: Sine signal.
- function3: Excitation signal. If not measured, enter zero. The carrier frequency will need to be manually input.
- carrier_frequency: Manually entered carrier frequency of the excitation. Only used in function3 is set to zero.
- resolver_type: Enter 1 for variable reluctance and 2 for electromagnetic resolver.
- number_of_poles: Number of poles on the resolver. Used to scale the rpm output.

The rate of the modulation of the sine and cosine is proportional to the speed of the motor. *Figure 7* shows the results of the calculations.

The faster the rate of the amplitude modulation of the sine and cosine signals, the higher the speed of the electric motor.

In the example calculations shown in this article, both rpm and angle are calculated from encoder or resolver data. The angle data is used in the calculation of the degree difference, while rpm data is used as verification that the parameters used in the formula are correct.

To support this, there are similar functions in the Simcenter Testlab Time Signal Calculator that can output either angle or rpm (

It is not uncommon to know at least the approximate rpm of the spinning systems. This rpm knowledge can be used to verify that all entries used in the formula were correct (

By verifying the rpm is as expected, then there is greater confidence that the entries for number of pulses, number of poles, type of resolver, etc are correct.

**4. Encoder: Moments versus RPM**

The angular position of the final drive is calculated from the highlighted formulas in*Figure 10*:

The angular position of the final drive is calculated from the highlighted formulas in

The final drive angular position was measured using an encoder. Encoder is a generic name for a device that outputs a series of voltage pulses proportional to speed of a piece of rotating machinery. The time between pulses is used to calculate the rotational speed. As the rotational speed increases, the time between pulses becomes smaller.

Examples encoder devices include: lasers, optical probes, magnetic pickups, and incremental encoders are shown in

When measuring an encoder (produces multiple pulses per revolution) with Simcenter Testlab and Simcenter SCADAS hardware, two pieces of information are recorded: the time stamps of each pulse crossing (the “raw” trace), and the rpm that is calculated from these crossings.

An example of the resulting measurement is shown in

The two recordings from the encoder measurement (calculated rpm and raw data) are shown in

The raw speed signal consists of the time stamps (or moments in time) that each encoder pulse occurred. It is the most compact and precise form for storing the rpm or angle data.

In the Simcenter Testlab Time Signal Calculator, both rpm and angle data can be calculated from these time stamps or moments. Functions that have the word “MOMENTS” utilize the raw time stamps for their calculations (*Figure 14*).

In the Simcenter Testlab Time Signal Calculator, both rpm and angle data can be calculated from these time stamps or moments. Functions that have the word “MOMENTS” utilize the raw time stamps for their calculations (

When available, it is usually best to use the MOMENT based functions for calculating rpm or angle from an encoder. An example with a 1000 pulse per revolution encoder is shown in

More information about using encoders in Simcenter Testlab can be found in the following articles:

- Measuring RPM: Missing Pulses
- Zebra Tape Butt Joint Correction for Torsional Vibrations
- Angle Domain: What is it?
- Torsional Vibration: What is it?

With both the electric motor resolver and final drive encoder angular positions calculated, the angular difference is calculated in the next section.

**5. Angular Difference Results**

Formulas for subtracting the angular position of the electric motor and final drive are shown in*Figure 17*:

Formulas for subtracting the angular position of the electric motor and final drive are shown in

The electric motor (which drives the rotating system) and final drive have a gear ratio of approximately nine (9x) as shown in

Knowing the exact ratio (in this case 9.04545) will yield the most accurate results. After adjusting by the ratio, the two angular position traces are subtracted as shown in *Figure 19*.

After subtracting, the angle difference shows brief “glitch” or “judder”. This corresponds to areas of higher vibration in a nearby accelerometer measurement. The exact cause of these “glitches” to be investigated and understood.

Hope this article is helpful! Questions? Email scott.beebe@siemens.com

Hope this article is helpful! Questions? Email scott.beebe@siemens.com

**Related Rotating Machinery Dynamics links:**

- Index of Simcenter Testing Knowledge Articles
- What's an Order?
- Torsional Vibration: What is it?
- Tips and Tricks for Torsional Orders
- Zebra Tape Butt Joint Correction for Torsional Vibrations
- Measuring RPM: Missing Pulse Compensation
- Balancing: Static, Coupled, and Dynamic
- What is an Orbit Plot?
- Removing Spikes from RPM Signals
- Simcenter Testlab Signature
- Fixed Sampling versus Synchronous Sampling
- Order Cuts: How to Get the Correct Amplitude?
- Recalculating Levels with Orders Removed
- Tips and tricks for acquiring torsional orders
- Angle Domain Analysis
- Simcenter Testlab Combustion Analysis
- Harmonic Removal
- Simcenter Testlab: Colormap Displays
- Interpreting Colormaps
- Cycle to Cycle Averaging in Simcenter Testlab
- Noise and Vibration Based End of Line Testing
- Knock Detection Algorithm Development
- Simcenter Testlab: Switching Frequencies and Pulse Width Modulation (PWM) Signals
- Rotating Machinery Dynamics Seminar
- Gears: Rotating Machinery Dynamics Seminar
- Rotating Machinery YouTube Playlist