Improve math skills of your kids - Learn step-by-step arithmetic from Math games

Math: Unknown - Step-by-step math calculation game for iOS.

Math: Unknown is much more than a math game. It is a step-by-step math calculation game which will teach users how to calculate in the correct order rather than just asking only the final calculated results.

The app consists of four basic arithmetic operations which are addition, subtraction, multiplication and division. In order to get started, users who are new to arithmetic can learn from animated calculation guides showing step-by-step procedures of solving each type of operation. It is also helpful for experienced users as a quick reference.

Generally, addition and subtraction may be difficult for users who just start learning math especially when questions require carrying or borrowing (also called regrouping). The app helps users to visualize the process of carrying and borrowing in the way it will be done on paper. Once users understand how these operations work, they are ready to learn multiplication and division.

For most students, division is considered as the most difficult arithmetic operation to solve. It is a common area of struggle since it requires prior knowledge of both multiplication and subtraction. To help users understand division, the app uses long division to teach all calculation procedures. Relevant multiplication table will be shown beside the question. Users will have to pick a number from the table which go into the dividend. Multiplication of selected number and divisor is automatically calculated, but the users have to do subtraction and drop down the next digit themselves. Learning whole calculation processes will make them master it in no time.

Math: Unknown is a helpful app for students who seriously want to improve arithmetic calculation skills.

Cam Follower Selection

Needle Roller Cam Followers

Needle Roller Cam Followers have a heavy outer ring cross section and a full complement of needle rollers. They offer high dynamic and static load carrying capability, and anti-friction performance, in a compact design. They are used as track rollers, cam followers, and in a wide range of linear motion systems.

Standard Stud cam followers offer the mounting convenience of a threaded stud and are designed to accommodate moderate loads. They are available with and without seals. Standard stud cam followers are also available with crowned outer rings for applications where misalignment is a problem.

Heavy Stud cam followers are designed to provide additional stud strength for applications with
high loading or shock loads. Heavy stud cam followers are available with and without seals, and with crowned outer rings.

Yoke Type cam followers are intended primarily for applications where loading conditions
exceed the capabilities of stud type cam followers, or where clevis mounting is desired. Clevis mounting provides support on both sides of the cam follower and permits use of a high strength pin. Yoke type cam followers are available with and without seals, and with crowned
outer rings.

CamCentric® adjustable cam followers (page 18) are used where accurate positioning is required. They are particularly useful for reducing clearance or backlash in opposed arrangements, and for assuring load sharing in multiple cam follower installations. Seals and hex socket are standard features of CamCentric® adjustable cam followers. Crowned outer rings are also available.

Crowned Outer Rings are used to minimize outer ring thrusting in applications where the axis of the cam follower is not parallel to the surface of the track or is skewed relative to the direction of travel. Crowned outer rings are a good selection for use with curved or circular tracks. In well aligned applications, crowned outer rings can cause accelerated track wear.

Cam Followers, Yoke, and Track Rollers

1. Difference from Standard Bearings

The outer rings of regular ball and roller bearings are typically mounted in rigid housings providing support around the entire circumference. Individual roller forces are transmitted through the outer ring directly into the housing with no major deformations.

By contrast, cam followers and yoke rollers are supported at a single point on their circumference. Individual roller forces produce bending moments on the outer ring around the point of contact. The effects are outer ring deformation with reversed bending stresses in dynamic applications, a reduced load zone, and a higher maximum roller load (see Fig. 1.).

To keep deformation to a minimum, the outer ring of a cam follower must have a considerably heavier cross section than a standard bearing. This requirement conflicts with the desire for maximum dynamic bearing capacity which needs as large a roller diameter as possible. RBC cam followers and yoke rollers provide an optimum compromise between outer ring strength and theoretical bearing capacity.

2. Capacity and Load Limits

Evaluation of the expected service life and limit loads of cam followers is more complex than with housed bearings. In addition to the static and dynamic capacity of the rolling elements, outer ring deformation, track capacity, and cam follower stud bending stress must be considered. In yoke rollers, the pin shear stress must be considered.

RBC lists the static bearing capacity for reference purposes only. Typically, the maximum allowable load is a function of the maximum permissible bending stress of the stud or the outer ring. For best results, the operating loads should not exceed the lower of track capacity or 50% of the dynamic capacity.

2.1 Capacity of Rolling Element Bearing

Equations for static and dynamic capacities of roller bearings are given in ANSI/ABMA Standard 11. The more recent revisions leave it up to the manufacturer to introduce factors which account for internal design features and operating conditions. For cam followers and yoke rollers RBC has chosen to apply a conservative rating system, so a direct comparison with capacity figures of competitive products may not be possible.

2.2 Track Capacity

Track capacity is that load which a track subject to a uniform contact stress can withstand without excessive plastic deformation. It is directly related to track hardness. The published track capacity is based on a hardness of HRc 40. For other track hardness values the track capacity must be modified with factors from Table 1.

Alternatively, contact stress can be easily calculated and compared directly to the strength of material. The equation for the Hertz contact stress between a cylindrical cam follower outer ring and a flat steel track is given by “Roark, Formulas for Stress and Strain” as:

It can be shown that for infinite life the ultimate tensile strength of track and roller must be at least equal to the maximum contact stress σC max

2.3. Bending and Shear Stresses

2.3.1 Cam Follower Stud Bending Stress

If the load over the width of the outer ring is evenly distributed, it may be replaced by a single
concentrated force F [lbf] acting at the center of the cam follower (see Fig.2). Assuming that the cam follower stud has been tightly mounted in a housing bore flush with the end plate, this concentrated force generates a bending moment Mb.

The bending moment generates a bending stress in the cam follower stud of approximate magnitude

Standard cam follower studs are heat treated to a hardness of HRc 58 min in the raceway area only.

The hardness in other areas of the stud is typically in a range of HRc 20 -22 with an ultimate strength of material of 110,000 -120,000 psi. RBC bases the maximum allowable load of stud type cam followers on a theoretical stud bending stress of 100,000 psi. Standard stud cam followers and heavy stud cam followers differ in stud diameter, which permits higher operating loads and more resistance to impact loading for the heavy stud version. High stud strength cam followers are available by special order.

In most applications the stud will deflect away from the load, which causes the point of attack to
shift toward the support, shortening the moment arm and reducing the effective bending moment (see Fig. 3). Tests show that this deflection yields a safety factor of at least 2 over RBC’s maximum allowable load. However, this effect may not be sufficient to avoid damage in severely misaligned applications where the load is applied at the very extreme outboard edge of the cam follower outer ring.

Where misalignment is a problem, RBC recommends crowned cam followers.

2.3.2 Yoke Roller Pin Shear Stress

Yoke rollers are mounted with a pin in a yoke. Under load the pin is subject to shear and bending
stresses. RBC recommends that the yoke arms are located as close to the yoke roller as possible, so that bending stress can be ignored. In case of widely spaced pin supports, the resulting pin deflection may cause yoke roller damage. The pin shear stress can be calculated with

The permissible stress depends on the pin material selection.


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