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   Four Bar Linkage - Design Methods
  Gears - Description
   Gears - General Gearing Arrangements
   Design Considerations
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   Lost Motion
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Gears - Description

Gear trains and gearing linkage exist in almost all flight control applications and are therefore important to understand. Furthermore, an understanding of gear train fundamentals provides the framework for analyzing all mechanical system linkages. In aerospace, gearing systems are used in electromechanical actuators (refer to Actuator, Electromechanical – Description), hydraulic pump and motor gearboxes, nosewheel steering drives and other applications. The typical purpose of the gearing system is to take a low torque, high speed motor and gear this down to a high torque, low speed at a flight surface, flap torque shaft, nosewheel steering strut, etc. In effect, speed is exchanged for an increase in torque.

For gear terminology, refer to Figure 1.

Figure 1 Gear Terminology

The circular pitch is the arc distance along pitch circle from a point on 1 gear tooth to the same point on the next gear tooth (from pt A to pt B in the figure). The circular pitch is computed using

where D is the pitch circle diameter and N is the number of gear teeth.

Figure 2 Two Gear Mesh

Figure 2 shows two gears meshed together. In Figure 2,

The gear ratio relationships are given below. Derivation of these relationships can be found in Gears – Equations.

An examination of the above gear ratio relationships shows that if T1 is low and θ1 is high, then T2 can be high and θ2 can be low. This is referred to as gearing down of the motor output, which allows a lighter, smaller, high speed, low torque motor to be used to apply larger loads at a slower rate to, say, a spoiler panel or trim tab. Effects of inertia, friction and efficiency through a gear train are discussed in Gears – Equations.

The goal of gear design is normally to match a desired angular velocity ratio. A velocity ratio can be specified directly or via a force/torque transfer relationships (see mechanical advantage discussion in Mechanisms - Mechanical Advantage). A designer can choose to use 2 gears, a multi-gear train, compound gear train or a planetary gear train to achieve a desired velocity ratio. The choice depends on desired velocity ratio, space constraints and general design guidelines for gears and gear teeth. Further details on gearing systems (multi-gear trains, compound gear trains and planetary gear trains) can be found in Gears – General Gearing Arrangements.

Gear Backlash

Backlash and deadzone are characteristics of gear trains and general mechanisms. From an analysis point of view, backlash is a nonlinear behavior and excessive backlash can reduce mechanism performance and cause closed loop instability. Physically, backlash is caused by our inability to manufacture perfect parts. As a result, there must be some clearance between gear teeth, as shown in Figure 3. In Figure 3, the input gear must travel a distance b/2 before contacting the output gear to impact motion. When the input gear has contacted the output gear and reverses direction, the input gear must travel a distance b before the output gear will start to move.

Figure 3 Gear Backlash

Anti-backlash gears are available and have been used in some aerospace applications. One method for a anti-backlash gear design cuts a gear into two halves, which each half being ½ of the thickness of the original gear. One of the gear halves is fixed to the shaft and the other gear half is allowed to rotate on the shaft. Several coil springs are then used to push the 2 gear halves apart (radially) so that the gear teeth fit tight between the teeth of the mating gear. The coil springs are sized such that compression of the springs is above the normal operating torque of the gear. An example of an anti-backlash gear set is shown in Figure 4.

Figure 4 Anti-Backlash Gear

Design Considerations

The selection of gear materials is very important, especially in applications where the gear train is part of a critical load path. In aerospace, materials for gears are normally a case hardened steel. Steel generally provides the best strength properties and it is durable from a fatigue standpoint. Case (surface hardening) of the gear teeth surface improves wear characteristics and reduces chances of galling in service. For critical applications, freeplay requirements are very tight and wear characteristics are important. Hardening is often used to ensure the gear teeth don’t wear in service. In non-critical applications, which also are low load, other materials may be used. In some applications, plastic gears may be used. Any choice of material should be examined from a static strength, fatigue, wear and environmental standpoint. The main environmental concerns are thermal affects, vibration and corrosion. Bearings used to support gears should also be of high quality, such as military or aerospace standard.

Surface or case hardening of gear teeth surfaces can be used to maximize wear characteristics, provide good surface stability and reduce backlash. Surface hardening is a material processing technique for increasing the (Rockwell) hardness of gear teeth surface. Surface hardening normally involves introducing carbon (at high temperature) into a low carbon steel thereby increasing the hardness for a thin material layer around the part. The purpose is to improve the wear characteristics of the gear teeth. The process for hardening is usually done after heat treat. Surface (case) hardening processes should be examined closely as there is a potential to induce hydrogen embrittlement in the material. It is important that the surface hardening process does not affect the heat treat and material properties of the base metal. Two methods for gear teeth hardening are carburization (carbon is introduced into the material surface) and nitriding (nitrogen is introduced into the material surface). Other surface hardening methods exist.

During manufacture, a good practice for critical load path gears is to send a material coupon through with a batch of gears during heat treat and case hardening. The coupon – blank metal about the same size of the gear – can then be inspected to ensure the heat treat and surface hardening processes were done properly. Destructive inspection methods on the coupon are used to verify proper material properties for the batch of gears.

Sizing of gears from a stress and fatigue point of view should take into account (i) heat generated during operation, (ii) static strength margin of the teeth, (iii) fatigue capability, (iv) abrasive wear characteristics of the gear material over the expected life, and (v) noise/vibration affects during operation. Gear teeth can be analyzed structurally treating each tooth has a cantilever beam. Special formulas are available in various gear design handbooks and AGMA standards.

When evaluating a gear train for a given application the following parameters should be considered in the evaluation.

Torque, Limit (or Max Operating) – Limit torque is the maximum torque the gear train must be able to provide at the output. Limit load is used as a static load to size the gear teeth. Ultimate load will be 1.5 times limit load. In some cases, specifications will give a limit load that is above max operating load by a certain factor (10-25% higher). Therefore, it is important to ensure limit load, maximum operating load and ultimate load are clearly defined when specifying or analyzing a gear train.

Endurance and Fatigue Loads – Endurance and fatigue loads represent the normal operating loads that a gear train would be expected to see over its operating life. Endurance and fatigue loads are usually the same spectrum. Endurance is associated with the gear train operating (rotating) and fatigue loads are associated with the gear train held statically. Like static loads, fatigue loads are used to size the gears through fatigue analysis. Gears with high load and low cycles will likely be sized by the static load while gears with requirements for high operational cycles will likely be sized by endurance loads. Endurance loads are normally associated with cycles (i.e., so many cycles at one load, so many cycles at another load and so on). Endurance tests are normally done with the gear train (or actuator) operating and fatigue loads are applied with the gear train static (not rotating). Fatigue requirements will specify the number of lives that a gear train must be tested. For example, if 1 life of endurance and 4 lives of fatigue testing are required a common practice is to do 1 life of endurance (gear train operating with endurance load spectrum applied) and 3 lives with the endurance/fatigue load applied with the gear train not operating (held statically). During fatigue testing the same gear teeth should be used (loaded) through the 3 or 4 lives of fatigue testing.

Bearings – Gears are mounted to shafts through bearings. The bearings should be rated for the expected loads (both static and fatigue) to be seen in service. High quality bearings, such as military or aerospace grade should be used in critical applications. In addition, the bearings will be more susceptible to environmental conditions than the gear. Therefore, careful assessments followed by appropriate environmental tests should be conducted to validate the bearing over the expected life of the gear train.

Gear Train Speed – The speed of gear train is not normally a big concern in aerospace gear train applications. However, gear trains have an upper RPM limit above which gear meshing may not occur properly and there may be excessive vibration leading to premature gear failure. Gear materials, gear teeth profiles, size of gear teeth, and amount of lubrication affect the maximum RPM limit.

Gear Material – Gear material should be chosen carefully. Steel is the usual choice for aerospace gears. The material is heat treated to achieve a desired hardness range (Rc 30 and above). For gear trains used in critical flight components, the material and process specifications should be clearly specified and the manufacturing process tightly controlled. In some cases, it may be necessary to specify material properties tighter than the general material or heat treat specifications.

Surface (Case) Hardening – Surface hardening will likely be required for critical gear train applications. The 2 most important aspects are to ensure proper specifications are in place to define the surface hardening process and that proper checks are done during manufacture to ensure the surface hardening process only hardens the outermost surface (usually around a few thousands of an inch) of the gear teeth. Sending test coupons through the hardening process with a each batch of gears is a good method to allow inspection of the process without having to destroy an expensive machined part. A qualified metallurgist should review all material process specifications.

Surface Finish – For gear trains to work at highest efficiency, the running surface finish should be as smooth as possible. Surface plating of gear teeth surfaces is not a good idea because of the potential for flaking of the finish, which will lead to increased and accelerated wear on the surfaces as well as bearing contamination.

Temperature – In aerospace applications, gear trains operate over a wide temperature range. Material properties can change over the full range. In addition, thermal expansion and contraction may lead to binding during operation. Both of these aspects should be validated in a gear train application via test.

Backlash (Freeplay) – A gear train will always contain a specification for backlash or freeplay. Backlash or freeplay is determined by applying a small torque in one direction and then measuring the distance the output gear moves when applying the same torque in the opposite direction. In measuring freeplay, the torque should be small enough so that structural deflections are not occurring (a few percent of maximum load is usually sufficient). Also, freeplay is a measure of control accuracy. Anti-backlash gears can be used to reduce freeplay.

Lubrication – Most gear trains and bearings are lubricated and require periodic lubrication when in service. Both the type of lubrication (normally grease) should be examined for compatibility with the materials. Periodic lubrication intervals should be established on the basis of test or service experience with similar gear train applications. Endurance testing is good approach for validating a chosen grease and a lubrication interval.

Life - Gear trains are designed for a certain life at a given load. Validation of the life capability of a gear train should be validated by endurance and fatigue tests.

Efficiency – Efficiency affects the input power requirements for a power screw. Efficiency requirements of the gear train will affect the design and sizing of the gear arrangements and the number of gear meshes. More gears lead to lower overall efficiency, as there is a 3-5% power loss for every gear mesh interface due to bearing friction and friction between the gear teeth. Bearing characteristics at temperature and under load should be evaluated to ensure bearing friction is low under all expected operating conditions.

Qualification testing for gears and gearboxes should include all of the mechanical environmental tests required by RTCA/DO-160 or Mil-Std-810 or other appropriate environmental specification. Normally environmental tests will be done at the actuator or component level. For example, if a gearbox is incorporated into an actuator, qualification will include other components such as a power screw, gearbox, any no-back device and any electronics installed in the actuator.