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Gear Transmission: How Small Gears Rotate the Big World
Gear transmission is one of the most common ways to transmit power and motion in mechanical engineering. It realizes energy transfer through the meshing of two or more gears, featuring high transmission efficiency, a wide power range, and stable transmission ratio. Its core principle revolves around "meshing transmission". This article elaborates on it from several aspects in detail.
Basic Composition and Meshing Fundamentals
1.1 Core Components
A gear consists of parts such as teeth, tooth grooves, addendum circle, and dedendum circle. The shape of the teeth (usually involute) is crucial for ensuring smooth transmission.
1.2 Meshing Principle
When two gears mesh with each other, the teeth of the driving gear push the teeth of the driven gear, transmitting rotational motion and torque from the driving gear to the driven gear. At this time, the contact point of the two gears is called the "meshing point", and the meshing point is always on the "meshing line" of the two gears, ensuring a constant transmission ratio.
a) Formation of Involute Tooth Profile
Most modern gears use involute as the tooth profile curve, and its formation principle is as follows:
An involute is the trajectory of any point on a straight line (generating line) when it rolls purely along a circle (base circle). The involute has the following important characteristics:
An involute is the trajectory of any point on a straight line (generating line) when it rolls purely along a circle (base circle). The involute has the following important characteristics:
- The meshing line is a straight line: The trajectory of the meshing point of the two gears is a fixed straight line.
- Constant transmission ratio: Ensures the smoothness of transmission.
- Divisibility of center distance: Changes in center distance do not affect the transmission ratio.
- Constant force direction: The pressure angle remains unchanged during meshing.
b) Basic Law of Gear Meshing
To keep the transmission ratio of a pair of gears constant, the basic law of tooth profile meshing must be satisfied:
When the tooth profiles of two gears are in contact at any position, the common normal line through the contact point must pass through the pitch point P (i.e., the tangent point of the two pitch circles);
The involute tooth profile fully satisfies this law, thus ensuring a constant transmission ratio.
When the tooth profiles of two gears are in contact at any position, the common normal line through the contact point must pass through the pitch point P (i.e., the tangent point of the two pitch circles);
The involute tooth profile fully satisfies this law, thus ensuring a constant transmission ratio.
1.3 Basic Characteristics of Gear Transmission
- Constant transmission ratio: The instantaneous transmission ratio of gear transmission is constant, ensuring smooth transmission.
- High transmission efficiency: The efficiency of general cylindrical gear transmission can reach 98% - 99.5%.
- Compact structure: Compared with other transmission methods, it requires less space under the same power and speed ratio.
- Reliable operation: A reasonably designed gear transmission can have a service life of several years or even decades.
- Wide application range: The power ranges from a fraction of a watt to tens of thousands of watts, and the circumferential speed ranges from extremely low to 300m/s.
Gear Transmission Ratio Relationship
2.1 Main Geometric Parameters
- Module (m): The basic dimension parameter of a gear, in mm. The larger the module, the larger the gear size.
- Number of teeth (z): The total number of teeth on the gear.
- Pressure angle (α): The standard value is 20°, which is an important parameter for the direction of the gear transmission force.
- Addendum coefficient (ha*): Usually 1.
- Clearance coefficient (c*): Usually 0.25.
2.2 Important Calculation Formulas
- Pitch circle diameter: d = m × z
- Addendum circle diameter: da = d + 2ha = m(z + 2ha*)
- Dedendum circle diameter: df = d - 2hf = m(z - 2ha* - 2c*)
- Base circle diameter: db = d × cosα
- Standard center distance: a = (d1 + d2)/2 = m(z1 + z2)/2
2.3 Transmission Ratio Formula
The transmission ratio (i) is the ratio of the rotational speed of the driving wheel (n₁) to the rotational speed of the driven wheel (n₂), and it is also equal to the ratio of the number of teeth of the driven wheel (z₂) to the number of teeth of the driving wheel (z₁), that is:
i = n₁/n₂ = z₂/z₁
For example, if the number of teeth of the driving wheel is 20 and that of the driven wheel is 40, the transmission ratio i = 2, which means that when the driving wheel rotates 2 circles, the driven wheel rotates 1 circle.
i = n₁/n₂ = z₂/z₁
For example, if the number of teeth of the driving wheel is 20 and that of the driven wheel is 40, the transmission ratio i = 2, which means that when the driving wheel rotates 2 circles, the driven wheel rotates 1 circle.
2.4 Direction Relationship
The direction of rotation of externally meshed gears (gears that are convex outward and mesh with each other) is opposite; the direction of rotation of internally meshed gears (one gear meshes inside another gear) is the same.
- Accurate transmission ratio: The number of gear teeth is fixed, and the transmission ratio is constant, which is suitable for scenarios that require precise control of rotational speed (such as machine tools, automobile gearboxes).
- High efficiency: The energy loss of meshing transmission is small, and the mechanical efficiency is usually between 90% and 99%.
- Wide power range: It can transmit from small power (such as clock gears) to super large power (such as ship propulsion gears).
- Compact structure: Compared with belt transmission and chain transmission, the structure of gear transmission is more compact under the same transmission ratio.
2.5 Analysis of Meshing Process
The meshing process of a pair of involute gears can be divided into three stages:
- Engagement stage: The addendum of the driven gear starts to contact with the dedendum of the driving gear.
- Normal meshing stage: The two tooth surfaces are in continuous contact on the meshing line.
- Disengagement stage: The addendum of the driving gear is separated from the dedendum of the driven gear.
Dynamics of Gear Transmission
In gear transmission, the driving gear exerts a "circumferential force" on the driven gear to push the driven gear to rotate. At the same time, there are also "radial force" (perpendicular to the gear axis) and "axial force" (parallel to the gear axis, existing only in non-straight bevel gears such as helical gears and bevel gears) between the two gears. Spur gears have no axial force and transmit more smoothly; although helical gears have axial force due to the inclination of the tooth surface, their meshing is tighter and their load-carrying capacity is stronger.
3.1 Gear Force Analysis
The main acting force in gear transmission is the normal force Fn along the meshing line direction, which can be decomposed into:
- Circumferential force Ft: Ft = 2T/d (T is torque)
- Radial force Fr: Fr = Ft × tanα
- Axial force Fa: Exists in helical gears, Fa = Ft × tanβ (β is the helix angle)
Gear Transmission Lubrication and Maintenance
4.1 Selection of Lubrication Methods
- Oil immersion lubrication: Suitable for gears with circumferential speed v ≤ 12m/s.
- Oil injection lubrication: Suitable for high-speed gears with v > 12m/s.
- Grease lubrication: Used in low-speed, light-load occasions or where it is inconvenient to use thin oil lubrication.
4.2 Common Faults and Treatment
- Tooth surface pitting: Improve tooth surface hardness and lubrication conditions.
- Gear tooth breakage: Increase the module and improve material toughness.
- Tooth surface wear: Improve lubrication conditions and increase tooth surface hardness.
- Tooth surface gluing: Use lubricating oil with strong anti-gluing ability.
Summary
Development Trends of Gear Transmission
- Application of high-strength materials: Such as high-strength alloy steel, powder metallurgy materials.
- High-precision manufacturing technology: Precision gear grinding, honing and other processes.
- New gear transmission: Such as circular arc gears, harmonic gears, planetary gears, etc.
- Integrated design: Integrated design with motors and reducers.
- Intelligent monitoring: Real-time monitoring of gear operation status using sensors.
As a basic component of mechanical transmission, the technical development of gear transmission directly affects the progress of the entire machinery industry. Gear transmission is developing towards higher precision, higher strength, longer service life and lower noise.
Pub Time : 2025-07-28 09:55:24
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