Developing a Mathematical Model of a Cyclone Gearbox

Compared to planetary gearboxes, cycloidal gearboxes are often seen as the ideal choice for a wide range of applications. They feature compact designs that are often low friction and high reduction ratios.

Low friction

Developing a mathematical model of a cycloidal gearbox was a challenge. The model was able to show the effects of a variety of geometric parameters on contact stresses. It was able to model stiction in all quadrants. It was able to show a clear correlation between the results from simulation and real-world measurements.
The model is based on a new approach that enables modeling stiction in all quadrants of a gearbox. It is also able to display non-zero current at standstill. Combined with a good simulation algorithm, the model can be used to improve the dynamic behaviour of a controlled system.
A cycloidal gearbox is a compact actuator used for industrial automation. This type of gearbox provides high gear ratios, low wear, and good torsional stiffness. In addition, it has good shock load capacity.
The model is based on cycloidal discs that engage with pins on a stationary ring gear. The resulting friction function occurs when the rotor begins to rotate. It also occurs when the rotor reverses its rotation. The model has two curves, one for motor and one for generator mode.
The trochoidal profile on the cycloidal disc’s periphery is required for proper mating of the rotating parts. In addition, the profile should be defined accurately. This will allow an even distribution of contact forces.
The model was used to compare the relative performance of a cycloidal gearbox with that of an involute gearbox. This comparison indicates that the cycloidal gearbox can withstand more load than an involute gearbox. It is also able to last longer. It is also able to produce high gear ratios in a small space.
The model used is able to capture the exact geometry of the parts. It can also allow a better analysis of stresses.

Compact

Unlike helical gearing, compact cycloidal gearboxes can provide higher reduction ratios. They are more compact and less weighty. In addition, they provide better positioning accuracy.
Cycloid drives provide high torque and load capacity. They are also very efficient and robust. They are ideal for applications with heavy loads or shock loads. They also feature low backlash and high torsional stiffness. Cycloid gearboxes are available in a variety of designs.
Cycloid discs are mounted on an eccentric input shaft, which drives them around a stationary ring gear. The ring gear consists of many pins, and the cycloidal disc moves one lobe for every rotation of the input shaft. The output shaft contains roller pins, which rotate around holes in the cycloidal disc.
Cycloid drives are ideally suited to heavy loads and shock loads. They have high torsional stiffness and high reduction ratios, making them very efficient. Cycloid gearboxes have low backlash and high torque and are very compact.
Cycloid gearboxes are used for a wide variety of applications, including marine propulsion systems, CNC machining centers, medical technology, and manipulation robots. They are especially useful in applications with critical positioning accuracy, such as surgical positioning systems. Cycloid gearboxes feature extremely low hysteresis loss and low backlash over extended periods of use.
Cycloid discs are usually designed with a reduced cycloid diameter to minimize unbalance forces at high speeds. Cycloid drives also feature minimal backlash, a high reduction ratio, and excellent positioning accuracy. Cycloid gearboxes also have a long service life, compared to other gear drives. Cycloid drives are highly robust, and offer higher reduction ratios than helical gear drives.
Cycloid gearboxes have a low cost and are easy to print. CZPT gearboxes are available in a wide range of sizes and can produce high torque on the output axis.

High reduction ratio

Among the types of gearboxes available, a high reduction ratio cycloidal gearbox is a popular choice in the automation field. This gearbox is used in applications requiring precise output and high efficiency.
Cycloid gears can provide high torque and transmit it well. They have low friction and a small backlash. They are widely used in robotic joints. However, they require special tools to manufacture. Some have even been 3D printed.
A cycloidal gearbox is typically a three-stage structure that includes an input hub, an output hub, and two cycloidal gears that rotate around each other. The input hub mounts movable pins and rollers, while the output hub mounts a stationary ring gear.
The input shaft is driven by an eccentric bearing. The disc is then pushed against the ring gear, which causes it to rotate around the bearing. As the disc rotates, the pins on the ring gear drive the pins on the output shaft.
The input shaft rotates a maximum of nine revolutions, while the output shaft rotates three revolutions. This means that the input shaft has to rotate over eleven million times before the output shaft is able to rotate. The output shaft also rotates in the opposite direction of the input shaft.
In a two-stage differential cycloidal speed reducer, the input shaft uses a crank shaft design. The crank shaft connects the first and second cycloidal gears and actuates them simultaneously.
The first stage is a cycloidal disc, which is a gear tooth profile. It has n=7 lobes on its circumference. Each lobe moves around a reference pitch circle of pins. The disc then advances in 360deg steps.
The second stage is a cycloidal disc, also known as a “grinder gear”. The teeth on the outer gear are fewer than the teeth on the inner gear. This allows the gear to be geardown based on the number of teeth.

Kinematics

Various scholars have studied the kinematics of cycloidal gearbox. They have developed various approaches to modify the tooth profile of cycloidal gears. Some of these approaches involve changing the shape of the cycloidal disc, and changing the grinding wheel center position.
This paper describes a new approach to cycloid gear profile modification. It is based on a mathematical model and incorporates several important parameters such as pressure angle, backlash, and root clearance. The study offers a new way for modification design of cycloid gears in precision reducers for robots.
The pressure angle of a tooth profile is an intersegment angle between the normal direction and the velocity direction at a meshing point. The pressure angle distribution is important for determining force transmission performance of gear teeth in meshing. The distribution trend can be obtained by calculating the equation (5).
The mathematical model for modification of the tooth profile can be obtained by establishing the relationship between the pressure angle distribution and the modification function. The dependent variable is the modification DL and the independent variable is the pressure angle a.
The position of the reference point A is a major consideration in the modification design. It ensures the force transmission performance of the meshing segment is optimal. It is determined by the smallest profile pressure angle. The position is also dependent on the type of gear that is being modified. It is also influenced by the tooth backlash.
The mathematical model governing the pressure angle distribution is developed with DL=f(a). It is a piecewise function that determines the pressure angle distribution of a tooth profile. It can also be expressed as DL=ph.
The pressure angle of a tooth is also an angle between the common normal direction at the meshing point and the rotation velocity direction of the cycloid gear.

Planetary gearboxes vs cycloidal gearboxes

Generally, there are two types of gearboxes that are used for motion control applications: cycloidal gearbox and planetary gearbox. Cycloid gearboxes are used for high-frequency motions, while planetary gearboxes are suitable for low-speed applications. Both are highly accurate and precise gearboxes that are capable of handling heavy loads at high cycle rates. But they have different advantages and disadvantages. So, engineers need to determine which type of gearbox is best suited for their application.
Cycloid gearboxes are commonly used in industrial automation. They provide excellent performance with ratios as low as 10:1. They offer a more compact design, higher torque density and greater overload protection. They also require less space and are less expensive than planetary gearboxes.
On the other hand, planetary gearboxes are lightweight and offer a higher torque density. They are also capable of handling higher ratios. They have a longer life span and are more precise and durable. They can be found in a variety of styles, including square-framed, round-framed and double-frame designs. They offer a wide range of torque and speed capabilities and are used for numerous applications.
Cycloid gearboxes can be manufactured with different types of cycloidal cams, including single or compound cycloidal cams. Cycloid cams are cylindrical elements that have cam followers that rotate in an eccentric fashion. The cam followers act like teeth on the internal gear. Cycloid cams are a simple concept, but they have numerous advantages. They have a low backlash over extended periods of time, allowing for more accurate positioning. They also have internal compressive stresses and an overlap factor between the rolling elements.
Planetary gearboxes are characterized by three basic force-transmitting elements: ring gear, sun gear, and planet gear. They are generally two-stage gearboxes. The sun gear is attached to the input shaft, which in turn is attached to the servomotor. The ring gear turns the sun gear and the planet gear turns the output shaft.

editor by CX 2023-11-07