Gyroscope Drift: Fundamentals and Impact on Accuracy
The basic function of a gyroscope is to provide a precise reference for measuring rotational motion. However, in actual gyroscopes, disturbance moments are always inevitably present, causing drift and nutation, thereby resulting in a change in the orientation of the rotation axis relative to the inertial space. In these two types of motion, the orientation change caused by nutation is extremely small and its influence can generally be ignored; while the orientation change caused by drift is more significant because it will cause the angular deviation of the rotation axis relative to the original inertial space to increase over time. Therefore, gyro drift is the main factor affecting the accuracy of the gyroscope.
Quantifying Drift: The Drift Rate
The speed and direction of gyroscope drift are represented by the drift angular velocity. The magnitude of the drift angular velocity is usually called the drift rate. When it is necessary to use the rotation axis to provide a certain orientation in the inertial space, the smaller the drift rate, the higher the stability accuracy of the orientation. When it is necessary to apply control forces to make the rotation axis track a certain changing orientation in space, the smaller the drift rate of the gyroscope, the higher the accuracy of orientation tracking. Therefore, the drift rate is the main indicator for measuring the accuracy of the gyroscope.
Mathematical Definition and Units of Drift Rate
Suppose the gyroscopic angular momentum is \( \boldsymbol{H} \), and the disturbing moment acting on the gyroscope is \( \boldsymbol{M_d} \). Then the value of the drift angular velocity is as expressed by this formula: \( \boldsymbol{\omega_d = \frac{M_d}{H}} \). From this formula, we can see that it is directly proportional to the disturbing moment and inversely proportional to the angular momentum. The unit of the drift rate is generally expressed as °/h or °/s. In the analysis of inertial navigation systems, sometimes the one-thousandth of the Earth’s rotational angular velocity is used as the unit of the drift rate, which is called a milli-earth-rate unit (abbreviated as meru), that is, 1 meru = 0.015°/h.
Classification of Disturbing Moments and Drift
Based on the nature and variation pattern of the disturbing moment, it can generally be classified into two types: one is the regular disturbing moment, and the other is the random disturbing moment. In gyroscopes, these two types of disturbing moments coexist simultaneously, so the gyro drift rate includes both the regular drift rate and the random drift rate.
Regular (Systematic) Drift Rate
The regular drift rate refers to the regular component in the drift rate. It is caused by the regular part of the disturbing moment, and its variation has a definite form and can be described by a deterministic functional relationship. For example, unbalanced moment, damping moment, elastic moment, non-isotropic elastic moment, etc. all belong to regular disturbing moments, and they will cause regular drift rates. Since the variation of this drift rate is regular, measures can be taken to compensate for it.
Random Drift Rate and Its Challenges
The random drift rate refers to the random component of the drift rate, that is, the irregular and time-varying component of the drift rate under specified operating conditions. It is caused by the random part of the disturbing moment. For example, the disturbing moments resulting from frictional forces and structural deformations are of a random nature. The variation pattern of the random drift rate does not have a definite form and cannot be described by a deterministic functional relationship. However, by using mathematical statistics methods, statistical analysis can be conducted on a large amount of drift data to identify statistical patterns. The random drift rate is usually represented by the standard deviation of each drift value. Since this drift rate is random, it cannot be compensated by conventional methods. Only by applying Kalman filtering technology can the influence of this random interference be greatly reduced. In the application of inertial navigation systems, the random drift rate of the gyroscope will seriously affect the positioning accuracy of the navigation system. Therefore, the inertial navigation system has strict requirements for the random drift rate of the gyroscope, and generally should reach 0.01°/h or even smaller.
Temporal Variations in Systematic Drift
In fact, the regular disturbing moment is not constant either. After being used for a period of time, its value may also change. Therefore, the regular disturbing moment also has the problem of random fluctuations.
Drift Rate Classification by Relation to Acceleration
If we consider the relationship between the disturbing moment and the acceleration (or specific force) of the vehicle, the drift rate can be classified into three categories: those independent of the acceleration (or specific force), those proportional to the acceleration (or specific force), and those proportional to the square of the acceleration (or specific force). For example, frictional moment, damping moment, elastic moment, and electromagnetic interference moment are independent of the acceleration. Unbalanced moment is proportional to the acceleration.The non-isotropic moment is proportional to the square of the acceleration. The so-called ratio force here refers to the resultant force of the gravitational force (caused by the gravitational field of celestial bodies in space) and the inertial force (caused by the acceleration of the moving body relative to the inertial space) acting on a unit mass.
Long-Term Stability: Run-to-Run Drift Rate
In addition, there is another type of random drift rate that characterizes the long-term stability of the gyroscope’s drift, called the run-to-run drift rate. It is mainly caused by the random changes in regular disturbing moments during each run-to-run startup. The run-to-run drift rate reflects the variation of the drift rate of the gyroscope in each operation. Depending on the sampling time interval, it can be divided into daily drift rate, monthly drift rate, and annual drift rate. The run-to-run drift rate is usually represented by the standard deviation of the drift rate values in each run.
Drift Rate Requirements by Application
Gyroscopes can be applied in various objects and systems. Depending on the specific application scenario, the requirements for gyro drift rate vary. Generally speaking, when used in indicating instruments or in flight control systems, the requirements for the accuracy of gyroscopes are relatively lower, and their drift rate requirements are typically in the range of several tens of degrees per hour to 1 degree per hour. When applied in aircraft and ship inertial navigation or strategic missile inertial guidance systems, the requirements for the accuracy of gyroscopes must be very high, and their drift rate requirements are generally 0.001 to 0.01°/h or even smaller (gyroscopes with drift rates less than 0.01°/h are often referred to as inertial-grade gyroscopes). Moreover, the longer the working time, the higher the requirements for the accuracy of gyroscopes. For example, the inertial navigation system used in nuclear submarines that remain submerged for a long time requires extremely low drift rate gyroscopes. In the following table, the approximate ranges of gyro drift rate requirements for various application objects and systems are listed.
| Applications | Required Drift Rate (°/h) |
|---|---|
| Vertical gyroscopes in flight control systems | 10–30 |
| Gyro horizons | 10–30 |
| Directional gyroscopes in flight control systems | 1–12 |
| Directional gyroscopes in gyro-magnetic compasses | 1–12 |
| Gyroscopes in tactical missile inertial guidance systems | 0.05–1 |
| Marine gyrocompasses | 0.01–0.2 |
| Gyroscopes in aircraft inertial navigation systems | 0.001–0.01 |
| Gyroscopes in ship inertial navigation systems | 0.001–0.01 |
| Gyroscopes in strategic missile inertial guidance systems | 0.0005–0.01 |
Methods to Reduce Drift Rate: Minimizing Disturbing
To reduce the gyroscope drift rate, it is necessary to minimize the disturbing moments. There are many factors that cause disturbing moments in a gyroscope, such as friction on the supporting shaft of the frame, the imbalance of the gyroscope components, the non-isotropic elasticity of the structure, the contact friction or elastic constraints of the power transmission device, electromagnetic interference from electromagnetic components, and manufacturing process errors, etc. In the design, structure, materials and process of the gyroscope, various factors that cause disturbing moments should be minimized as much as possible. On the other hand, efforts are constantly being made to develop various new supporting methods and new working principles of gyros in order to achieve a lower drift rate. The approximate range of drift rates that various types of gyros can currently achieve is shown in the following table.
| Type of Gyroscope | Drift Rate Range (°/h) |
|---|---|
| Conventional Gyroscope | 30 to 1 |
| Rotorace Gyroscope | 1 to 0.1 |
| Fluid-floated Gyroscopes | 0.01 to 0.0001 |
| Gas-bearing Gyroscope | 0.01 to 0.001 |
| Dynamically Tuned Gyroscope (DTG) | 0.01 to 0.001 |
| Electrostatically Suspended Gyroscope (ESG) | 0.001 to 0.0001 |
Trade-offs in Increasing Angular Momentum
To reduce the gyroscope drift rate, it is necessary to appropriately increase the gyroscope angular momentum. This can be achieved by appropriately increasing the rotor’s moment of inertia and the self-rotation angular velocity. However, excessively increasing the angular momentum will bring adverse effects such as increased instrument size, mass, power consumption and heat generation, and it has no significant effect on reducing the drift rate. This is because as the mass increases, the disturbing moments related to the mass, such as bearing friction and center of mass deviation, also increase accordingly. Moreover, as the heat increases, the disturbing moments related to the heat, such as thermal deformation and thermal convection, also increase accordingly. As a result, the effect of increasing the angular momentum is largely offset by the increase in disturbing moments, and it may even have the opposite effect.