A Mathematical Model of a Cycloid Gearbox

Having a gearbox with a cycloidal rotor is an ideal design for a car or any other vehicle, as the cycloidal design can reduce the amplitude of vibration, which is a key component in car performance. Using a cycloidal gearbox is also a great way to reduce the amount of friction between the gears in the gearbox, which can help to reduce noise and wear and tear. A cycloidal gearbox is also a very efficient design for a vehicle that needs to perform under high loads, as the gearbox can be very robust against shock loads.

Basic design principles

cycloidal gearboxes are used for precision gearing applications. Cycloidal drives are compact and robust and offer lower backlash, torsional stiffness and a longer service life. They are also suitable for applications involving heavy loads.
Cycloidal drives are compact in size and provide very high reduction ratios. They are also very robust and can handle shock loads. Cycloidal drives are ideally suited to a wide range of drive technologies. Cycloidal gears have excellent torsional stiffness and can provide a transmission ratio of 300:1. They can also be used in applications where stacking multiple gear stages is not desired.
In order to achieve a high reduction ratio, cycloidal gears must be manufactured extremely accurately. Cycloidal gears have a curved tooth profile that removes shear forces at any point of contact. This provides a positive fit for the gear disc. This profile can be provided on a separate outer bushing or as an internal gear profile insert.
Cycloidal drives are used in marine propulsion systems, where the load plate rotates around the X and Y axis. The plate is anchored by a threaded screw hole arranged 15mm away from the center.
A secondary carrier body is used in a cycloidal gearbox to support the load plate. The secondary carrier body is composed of a mounting carrier body and a secondary carrier disc.

Low friction

Several studies have been conducted to understand the static problems of gears. In this paper, we discuss a mathematical model of a low friction cycloidal gearbox. This model is designed to calculate various parameters that affect the performance of the gearbox during production.
The model is based on a new approach that includes the stiction effect and the nonlinear friction characteristic. These parameters are not covered by the conventional rule of thumb.
The stiction effect is present when the speed direction is changed. During this time, the input torque is required to prevail over the stiction effect to generate movement. The model also enables us to calculate the magnitude of the stiction effect and its breakaway speed.
The most important thing is that the model can be used to improve the dynamic behavior of a controlled system. In this regard, the model has a high degree of accuracy. The model is tested in several quadrants of the gearbox to find the optimum stiction breakaway speed. The simulation results of the model show that this model is effective in predicting the efficiency of a low friction cycloidal gearbox.
In addition to the stiction model, we also studied the efficiency of a low friction cycloidal reducer. The reduction ratio of this gearbox was estimated from the formula. It is found that the ratio approaches negative infinity when the motor torque is close to zero Nm.

Compact

Unlike standard planetary gears, cycloidal gearboxes are compact, low friction and feature virtually zero backlash. They also offer high reduction ratios, high load capacity and high efficiency. These features make them a viable option for a variety of applications.
Cycloid disks are driven by an eccentric input shaft. They are then driven by a stationary ring gear. The ring gear rotates the cycloidal disk at a higher rate. The input shaft rotates nine times to complete a full rotation. The ring gear is designed to correct the dynamic imbalance.
CZPT cycloidal gearheads are designed for precision and stable operation. These reducers are robust and can handle large translocations. They also offer high overload protection. They are suitable for shock wave therapy. CZPT gearheads are also well suited for applications with critical positioning accuracy. They also require low assembly and design costs. They are designed for long service life and low hysteresis loss.
CZPT cycloidal reducers are used in a variety of industrial applications, including CNC machining centers, robot positioners and manipulators. They offer a unique design that can handle high forces on the output axis, and are especially suitable for large translocations. These gearheads are highly efficient, reducing costs, and are available in a variety of sizes. They are ideal for applications that require millimetre accuracy.

High reduction ratios

Compared to other gearboxes, cycloidal gearboxes offer high reduction ratios and small backlash. They are also less expensive. Cycloid gearboxes can be used in a variety of industries. They are suitable for robotic applications. They also have high efficiency and load capacity.
A cycloidal gearbox works by rotating a cycloidal disc. This disc contains holes that are bigger than the pins on the output shaft. When the disc is rotated, the output pins move in the holes to generate a steady output shaft rotation. This type of gearbox does not require stacking stages.
Cycloid gearboxes are usually shorter than planetary gearboxes. Moreover, they are more robust and can transmit higher torques.
Cycloid gearboxes have an eccentric cam that drives the cycloidal disc. The cycloidal disc advances in 360deg/pivot/roller steps. It also rotates in an eccentric pattern. It meshes with the ring-gear housing. It also engages the internal teeth of the ring-gear housing.
The number of lobes on the cycloidal disc is not sufficient to generate a good transmission ratio. In fact, the number of lobes must be less than the number of pins surrounding the cycloidal disc.
The cycloidal disc is rotated by an eccentric cam that extends from the base shaft. The cam also spins inside the cycloidal disc. The eccentric motion of the cam helps the cycloidal disc rotate around the pins of the ring-gear housing.

Reducing amplitude of the vibration

Various approaches to reducing amplitude of the vibration in a cycloidal gearbox have been studied. These approaches are based on the kinematic analysis of gearbox.
A cycloidal gearbox is a gearbox that consists of bearings, gears, and an eccentric bearing that drives a cycloidal disc. This gearbox has a high reduction ratio, which is achieved by a series of output shaft pins that drive the output shaft as the disc rotates.
The test bench used in the studies has four sensors. Each sensor acquires signals with different signal processing techniques. In addition, there is a tachometer that acquires variations in rotational velocity at the input side.
The kinematic study of the robotic gearbox was performed to understand the frequency of vibrations and to determine whether the gearbox is faulty. It was found that the gearbox is in healthy operation when the amplitude of the x and y is low. However, when the amplitude is high, it is indicative of a malfunctioning element.
The frequency analysis of vibration signals is performed for both cyclostationary and noncyclostationary conditions. The frequencies that are selected are those that appear in both types of conditions.

Robust against shock loads

Compared to traditional gearboxes, cycloidal gearboxes have significant benefits when it comes to shock loads. These include high shock-load capacity, high efficiency, reduced cost, lower weight, lower friction, and better positioning accuracy.
Cycloid gears can be used to replace traditional planetary gears in applications where inertia is important, such as the transportation of heavy loads. They have a lighter design and can be manufactured to a more compact size, which helps reduce cost and installation expense. Cycloid gears are also able to provide transmission ratios of up to 300:1 in a small package.
Cycloid gears are also suitable for applications where a long service life is essential. Their radial clamping ring reduces inertia by up to 39%. Cycloid gears have a torsional stiffness that is five times higher than that of conventional planetary gears.
Cycloid gearboxes can provide significant improvements in concrete mixers. They are a highly efficient design, which allows for important innovations. They are also ideal for servo applications, machine tools, and medical technology. They feature user-friendly screw connections, effective corrosion protection, and effective handling.
Cycloid gears are especially useful for applications with critical positioning accuracy. For example, in the control of large parabolic antennas, high shock load capacity is required to maintain accuracy. Cycloid gears can withstand shock loads up to 500% of their rated torque.

Inertial effects

Various studies have been conducted to investigate the static problems of gears. However, there is still a need for a proper model to investigate the dynamic behaviour of a controlled system. For this, a mathematical model of a cycloidal gearbox has been developed. The presented model is a simple model that can be used as the basis for a more complex mechanical model.
The mathematical model is based on the cycloidal gearbox’s mechanical construction and has a nonlinear friction characteristic. The model is able to reproduce the current peaks and breaks at standstill. It also considers the stiction effect. However, it does not cover backlash or torsional stiffness.
This model is used to calculate the torque generating current and the inertia of the motor. These values are then compared with the real system measurement. The results show that the simulation results are very close to the real system measurement.
Several parameters are considered in the model to improve its dynamic behaviour. These parameters are calculated from the harmonic drive system analysis. These are torque-generating current, inertia, and the contact forces of the rotating parts.
The model has a high level of accuracy and can be used for motor control. It is also able to reproduce the dynamic behaviour of a controlled system.

editor by CX 2023-11-10